Symmetry-protecting ansatz for the variational quantum eigensolver of mirror- and occupation-number-inversion-symmetrical systems

The variational quantum eigensolver (VQE) is considered one of the most powerful alternative approaches for near-term noisy intermediate-scale quantum devices. However, the successful implementation of the VQE is quite challenging, as the ansatz must be sufficiently expressive, yet, if it is overly expressive, it may hinder the optimization process of the VQE in finding the global minimum. To address this challenge of the VQE, a commonly used approach is to apply the symmetries of the system, which reduces the dimensionality of the parameter space for the VQE. Here, we propose a quantum circuit that can be used for systems with mirror symmetry and occupation-number-inversion symmetry. We demonstrate its usefulness by applying it to find the eigenenergies of the Anderson impurity model, a representative fundamental model for various quantum simulations. In addition, we demonstrate the usability of our quantum circuit by applying it to a quantum algorithm for Green's function, which plays a crucial role in understanding quantum systems of condensed matter physics.